A dental-jet device of the type defined in the first paragraph and a mouthpiece of the type defined in the second paragraph are known, for example from DE-A1-35 26 579. In the known dental-jet device and the known mouthpiece the tubular part has a widened end portion, which widened end portion engages with an intermediate portion of the tubular part. The intermediate portion has a plurality of flow channels, in and also has mounted therein a jet insert of the tubular part. The insert has ports for the supply of fluid, i.e. of water, to the peripheral-jet orifices in the nozzle head and has a passage for the supply of fluid, i.e. of water, to a central-jet orifice in the nozzle head. The jet insert of the tubular part has a surface transverse to the axis of rotation of the nozzle head which simply engages with a nozzle-head surface transverse to the axis of rotation of the nozzle head. As a result of this construction, water undesirably discharges from the peripheral-jet orifices when the nozzle head is in its central-jet position and consequently loss of volume and loss of pressure occur in the water jet emerging from the central-jet orifice. Apart from this undesired property of the known dental-jet device and the known mouthpiece, it is also unfavourable that the known mouthpiece of the known dental-jet device is of a comparatively intricate construction, comprising a comparatively large number of parts.